Multidimensional Stability of Planar Viscous Shock Waves

Physical and mathematical considerations warrant the inclusion of regularizing effects such as diffusion, dissipation, and/or relaxation in the study of stability of shock waves, particularly in MHD, combustion, and multiphase flow. Indeed, in this generality, the “ideal shock” approximation has relevance only in the long-wave limit, that is, in the large, but not in the small scale. Likewise, multidimensional effects are known both from experiment and from the study of the inviscid (hyperbolic) case to play a key role in determining stability. Yet, until very recently, there were no rigorous analyses for systems taking into account both effects simultaneously.